A Novel Portfolio Based on Interval-Valued Intuitionistic Fuzzy AHP with Improved Combination Weight Method and New Score Function

Abstract

The classical Analytic Hierarchy Process (AHP) requires an exact value to compare the relative importance of two attributes, but experts often can not obtain an accurate assessment of every attribute in the decision-making process, there are always some uncertainty and hesitation. Compared with classical AHP, our new defined interval-valued intuitionistic fuzzy AHP has accurately descripted the vagueness and uncertainty. In decision matrix, the real numbers are substituted by fuzzy numbers. In addition, each expert will make different evaluations according to different experiences for each attribute in the subjective weighting method, which neglects objective factors and then generates some deviations in some cases. This paper provides two ways to make up for this disadvantage. On the one hand, by combining the interval-valued intuitionistic fuzzy AHP with entropy weight, an improved combination weighting method is proposed, which can overcome the limitations of unilateral weighted method only considering the objective or subjective factors. On the other hand, a new score function is presented by adjusting the parameters, which can overcome the invalidity of some existing score functions. In theory, some theorems and properties for the new score functions are given with strictly mathematical proof to validate its rationality and effectiveness. In application, a novel fuzzy portfolio is proposed based on the improved combination weighted method and new score function. A numerical example shows that these results of our new score function are consistent with those of most existing score functions, which verifies that our model is feasible and effective.